EduSahara™ Worksheet

Question 1

1.

Two poles of equal height are standing opposite to each other on either side of a road which is 5 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 45° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

4.17 m

, distances away =

4.17 m

,

2.83 m
(ii)
height =

1.17 m

, distances away =

1.17 m

,

9.83 m
(iii)
height =

3.17 m

, distances away =

3.17 m

,

1.83 m
(iv)
height =

2.17 m

, distances away =

2.17 m

,

0.83 m
(v)
height =

5.17 m

, distances away =

5.17 m

,

3.83 m

Question 2

2.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60° with the ground. The top of the tree touches the ground at a distance of 50 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

186.61 m
(ii)

160.61 m
(iii)

201.61 m
(iv)

214.61 m
(v)

179.61 m

Question 3

3.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?

(i)

∠c
(ii)

∠e
(iii)

∠d
(iv)

∠b

Question 4

4.

From the top of a light house which is 50 m high from the sea level, the angles of depression of two ships are 60° and 45°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.

(i)

18.13 m
(ii)

24.13 m
(iii)

26.13 m
(iv)

16.13 m
(v)

21.13 m

Question 5

5.

From a point 120 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 30° respectively. Find the height of the pillar.

(i)

123.56 m
(ii)

151.56 m
(iii)

110.56 m
(iv)

138.56 m
(v)

165.56 m

Question 6

6.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
60°
.
If the height of the
radio tower
is
140 m
,
find the distance between
the observation point and the foot of the
radio tower
.

(i)

140
3

m
(ii)

140
3

√

3

m
(iii)

70

√

2

m
(iv)

140
3

√

18

m
(v)

140

m

Question 7

7.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 120 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 60° respectively. Find the height of the other temple.

(i)

77.00 m
(ii)

75.00 m
(iii)

80.00 m
(iv)

85.00 m
(v)

83.00 m

Question 8

8.

The angles of depression of two boats from the top of a cliff 190 m high are 60° and 45° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

277.71 m
(ii)

315.71 m
(iii)

311.71 m
(iv)

293.71 m
(v)

299.71 m

Question 9

9.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
60°
.
If the distance between the point and the top of the
radio tower
is
90 m
,
find the distance between
the observation point and the foot of the
radio tower
.

(i)

43

m
(ii)

47

m
(iii)

44

m
(iv)

46

m
(v)

45

m

Question 10

10.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 140 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 60° respectively. Find the width of the river .

(i)

77.83 m
(ii)

83.83 m
(iii)

85.83 m
(iv)

80.83 m
(v)

75.83 m

Question 11

11.

Two boys are on opposite sides of a tower of 100 m height. They measure the angle of elevation of the top of the tower as 30° and 45° respectively. Find the distance between the two boys.

(i)

(

150

√

2

+

50

√

6

)

m
(ii)

20000

m
(iii)

(

100

√

3

+

100

)

m
(iv)

(

2

+

√

3

)

m
(v)

(

100

√

18

+

100

√

6

)

m

Question 12

12.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
60°
.
If the height of the
building
is
30 m
,
find the distance between
the observation point and the top of the
building
.

(i)

20

m
(ii)

20

√

3

m
(iii)

30

√

2

m
(iv)

20

√

18

m
(v)

60

m

Question 13

13.

A flagstaff stands on the top of a building at a distance of 40 m away from the foot of building . The angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 45°. Find the height of the flagstaff .

(i)

(

2

−

√

3

)

m
(ii)

3200

m
(iii)

(

40

√

3

−

40

)

m
(iv)

(

60

√

2

−

20

√

6

)

m
(v)

(

40

√

18

−

40

√

6

)

m

Question 14

14.

A man 1.3 m tall stands at a distance of 5.6 m from a lamp post and casts a shadow of 3.1 m on the ground. Find the height of the lamp post .

(i)

5.65 m
(ii)

4.65 m
(iii)

1.65 m
(iv)

3.65 m
(v)

2.65 m

Question 15

15.

An observer 1.3 m tall, is 60 m away from a tower . The angle of elevation of the top of the tower from her eyes is 60°. Find the height of the tower .

(i)

123.23 m
(ii)

98.23 m
(iii)

120.23 m
(iv)

105.23 m
(v)

91.23 m

Question 16

16.

From a point 180 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 30° respectively. Find the height of the cliff.

(i)

86.93 m
(ii)

103.93 m
(iii)

101.93 m
(iv)

109.93 m
(v)

116.93 m

Question 17

17.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 45° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 14 m, find the height of the building .

(i)

16.13 m
(ii)

24.13 m
(iii)

22.13 m
(iv)

14.13 m
(v)

19.13 m

Question 18

18.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
45°
.
If the distance between the point and the foot of the
radio tower
is
150 m
,
find the height of the
radio tower
.

(i)

152

m
(ii)

148

m
(iii)

150

m
(iv)

149

m
(v)

151

m

Question 19

19.

The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 45°. If the height of the tower is 90 m, find the height of the building .

(i)

46.97 m
(ii)

51.97 m
(iii)

56.97 m
(iv)

54.97 m
(v)

48.97 m

Question 20

20.

The angles of depression of two boats from the top of a cliff 60 m high are 30° and 60° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

69.28 m
(ii)

64.28 m
(iii)

72.28 m
(iv)

74.28 m
(v)

66.28 m

Question 21

21.

A
tower
stands vertically on the ground.

The distance between the observation point and its foot
tower
is
10

√

3

m
.

The distance between the observation point and its top
is
20

m
.

Find the angle of elevation.

(i)

60°
(ii)

30°
(iii)

45°
(iv)

75°
(v)

90°

Question 22

22.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
45°
.
If the distance between the point and the top of the
building
is
130 m
,
find the height of the
building
.

(i)

65

√

2

m
(ii)

130

m
(iii)

65

m
(iv)

130

√

3

m
(v)

65
2

√

12

m

Question 23

23.

Two vertical poles are on either side of a road. A 39 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 45° with the pole and when it is turned to rest against another pole, it makes an angle of 30° with the road. Find the width of the road.

(i)

66.35 m
(ii)

58.35 m
(iii)

64.35 m
(iv)

56.35 m
(v)

61.35 m

Question 24

24.

From the top of a 10 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Find the height of the cable tower.

(i)

27.32 m
(ii)

32.32 m
(iii)

24.32 m
(iv)

30.32 m
(v)

22.32 m

Question 25

25.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
60°
.
If the distance between the point and the foot of the
tower
is
60 m
,
find the distance between
the observation point and the top of the
tower
.

(i)

120

m
(ii)

123

m
(iii)

119

m
(iv)

121

m
(v)

118

m

Assignment Key